问题 解答题
先观察1-
1
22
=
1
2
×
3
2
1-
1
32
=
2
3
×
4
3
1-
1
42
=
3
4
×
5
4

(1)按上述规律填空:1-
1
1002
=______×______;1-
1
20102
=______×______.
(2)计算:(1-
1
22
)•(1-
1
32
)•(1-
1
42
)•…•(1-
1
20102
)
答案

(1)依题意,得1-

1
1002
=
99
100
×
101
100
1-
1
20102
=
2009
2010
×
2011
2010

故答案为:

99
100
101
100
2009
2010
2011
2010

(2)原式=

1
2
×
3
2
×
2
3
×
4
3
×
3
4
×
5
4
×…×
2009
2010
×
2011
2010

=

1
2
×
2011
2010

=

2011
4020

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